相关论文: The Largest Condorcet Domains on 8 Alternatives

In this paper we study optimization problems for Neumann eigenvalues $\mu_k$ among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, though some results are stated in higher dimension. We study…

A topological space is domain-representable (or, has a domain model) if it is homeomorphic to the maximal point space $\mbox{Max}(P)$ of a domain $P$ (with the relative Scott topology). We first construct an example to show that the set of…

We consider the problem of maximizing the volume of hermitian ellipsoids inscribed in a given pseudoconvex domain in complex Euclidean space. We prove existence and uniqueness, and give a characterization of the maximizer.

The diameter of a graph is the maximum distance between pairs of vertices in the graph. A pair of vertices whose distance is equal to its diameter are called diametrically opposite vertices. The collection of shortest paths between…

We define a statistic on the graph of commutation classes of a permutation of the symmetric group which is used to show that these graphs are equipped with a ranked poset structure, with a minimum and maximum. This characterization also…

Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…

Danilov, Karzanov and Koshevoy (2012) geometrically introduced an interesting operation of composition on tiling Condorcet domains and using it they disproved a long-standing problem of Fishburn about the maximal size of connected Condorcet…

The universal genetic code presents a fundamental paradox in molecular biology. Recent advances in synthetic biology have demonstrated that the code is remarkably flexible--organisms can survive with 61 codons instead of 64, natural…

Constraint programming (CP) is a powerful tool for modeling mathematical concepts and objects and finding both solutions or counter examples. One of the major strengths of CP is that problems can easily be combined or expanded. In this…

A symmetric subset of the reals is one that remains invariant under some reflection z --> c-z. We consider, for any 0 < x <= 1, the largest real number D(x) such that every subset of $[0,1]$ with measure greater than x contains a symmetric…

It is well known that the standard flat torus $\mathbb{T}^2=\mathbb{R}^2/\Z^2$ has arbitrarily large Laplacian-eigenvalue multiplicities. We prove, however, that $24$ is the optimal upper bound for the multiplicities of the nonzero…

Let $s$ denote West's stack-sorting map. A permutation is called $t-\textit{sorted}$ if it is of the form $s^t(\mu)$ for some permutation $\mu$. We prove that the maximum number of descents that a $t$-sorted permutation of length $n$ can…

The Condorcet criterion (CC) is a classical and well-accepted criterion for voting. Unfortunately, it is incompatible with many other desiderata including participation (Par), half-way monotonicity (HM), Maskin monotonicity (MM), and…

We show that each pseudoconvex domain $\Omega\subset {\mathbb C}^n$ admits a holomorphic map $F$ to ${\mathbb C}^m$ with $|F|\le C_1 e^{C_2 \hat{\delta}^{-6}}$, where $\hat{\delta}$ is the minimum of the boundary distance and…

Let $\C$ be a genus 2 curve defined over $k$, $char (k) =0$. If $\C$ has a $(3,3)$-split Jacobian then we show that the automorphism group $Aut(\C)$ is isomorphic to one of the following: $\bZ_2, V_4, D_8$, or $D_{12}$. There are exactly…

We investigate domain-wall/quantum field theory correspondences in various dimensions. Our general analysis does not only cover the well-studied cases in ten and eleven dimensions but also enables us to discuss new cases like a Type…

We prove that a face of a cube can be optimally partitioned into connected 193 sets on which the cut locus, or ridge tree, is constant up to isomorphism as a labeled graph. These are 60 connected open sets, curves bounding them, and…

We characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. In particular, we show the following. 1. Every preference profile with up to two voters is one-dimensional Euclidean if and only…

We present 226 large ultra-diffuse galaxy (UDG) candidates ($r_e > 5.3$\arcsec, $\mu_{0,g} > 24$ mag arcsec$^{-2}$) in the SDSS Stripe 82 region recovered using our improved procedure developed in anticipation of processing the entire…

Let $\textrm{S}(n,t,k)$ be the maximum size of a code containing only vectors of the $k$th shell of the integer lattice $\mathbb{Z}^n$ such that the inner product between distinct vectors does not exceed $t$. In this paper we compute lower…